Publications by Pedram Pad | EPFL Graph Search

Related publications (13)

On The Optimality Of Operator-Like Wavelets For Sparse Ar(1) Processes

Sinusoidal transforms such as the DCT are known to be optimal-that is, asymptotically equivalent to the Karhunen-Loeve transform (KLT)-for the representation of Gaussian stationary processes, including the classical AR(1) processes. While the KLT remains a ...

Ieee2013

Optimal Representations of Sparse Stochastic Processes with Applications in Image Processing

Pedram Pad

We establish in the world of stochastic processes a theoretical relation between sparsity and wavelets. The underlying principle is to treat stochastic processes as generalized functions, which facilitates the study of their properties in a transform domai ...

EPFL2017

Optimality of Operator-Like Wavelets for Representing Sparse AR(1) Processes

Michaël Unser, Pedram Pad

The discrete cosine transform (DCT) is known to be asymptotically equivalent to the Karhunen-Loève transform (KLT) of Gaussian first-order auto-regressive (AR(1)) processes. Since being uncorrelated under the Gaussian hypothesis is synonymous with independ ...

IEEE2015

Dictionary Learning Based on Sparse Distribution Tomography

Michaël Unser, Pedram Pad

We propose a new statistical dictionary learning algorithm for sparse signals that is based on an α-stable innovation model. The parameters of the underlying model—that is, the atoms of the dictionary, the sparsity index α and the dispersion of the transfo ...

P. Pad2017

MMSE Denoising of Sparse and Non-Gaussian AR(1) Processes

Michaël Unser, Emrah Bostan, Pedram Pad

We propose two minimum-mean-square-error (MMSE) estimation methods for denoising non-Gaussian first-order autoregressive (AR(1)) processes. The first one is based on the message passing framework and gives the exact theoretic MMSE estimator. The second is ...

IEEE2016

MMSE Estimation of Sparse Levy Processes

Michaël Unser, Ulugbek Kamilov, Arash Amini, Pedram Pad

We investigate a stochastic signal-processing framework for signals with sparse derivatives, where the samples of a Levy process are corrupted by noise. The proposed signal model covers the well-known Brownian motion and piecewise-constant Poisson process; ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Optimized Wavelet Denoising for Self-Similar alpha-Stable Processes

Michaël Unser, Pedram Pad

We investigate the performance of wavelet shrinkage methods for the denoising of symmetric-a-stable (S alpha S) self-similar stochastic processes corrupted by additive white Gaussian noise (AWGN), where a is tied to the sparsity of the process. The wavelet ...

2017

Optimized Steerable Wavelets for Texture Analysis of Lung Tissue In 3-D CT: Classification of Usual Interstitial Pneumonia

Michaël Unser, Adrien Raphaël Depeursinge, Pedram Pad

Our aim is to optimize wavelet-based feature extraction for differentiating between the classical versus atypical pattern of usual interstitial pneumonia (UIP) in volumetric CT. Our proposal is to act on the bandwidth of steerable wavelets while maintainin ...

IEEE2015

VOW: Variance-Optimal Wavelets for the Steerable Pyramid

Michaël Unser, Virginie Sophie Uhlmann, Pedram Pad

We study the issue of localization in the context of isotropic wavelet frames. We define a variance-type measure of localization and propose an algorithm based on calculus of variations to minimize this criterion under the constraint of a tight wavelet fra ...

IEEE2014

Matched Wavelet-Like Bases for the Decoupling of Sparse Stochastic Processes

Michaël Unser, Pedram Pad

SMAI-SIGMA2014

Maximally Localized Radial Profiles for Tight Steerable Wavelet Frames

Michaël Unser, Virginie Sophie Uhlmann, Pedram Pad

A crucial component of steerable wavelets is the radial profile of the generating function in the frequency domain. In this paper, we present an infinite-dimensional optimization scheme that helps us find the optimal profile for a given criterion over the ...

IEEE2016

A data-driven approach for lightning nowcasting with deep learning

Farhad Rachidi-Haeri, Marcos Rubinstein, Amirhossein Mostajabi, Pedram Pad, Seyed Mohammad Ehsan Mansouri Tehrani

2021

Optimal Isotropic Wavelets for Localized Tight Frame Representations

Michaël Unser, John Paul Ward, Pedram Pad

In this letter, we aim to identify the optimal isotropic mother wavelet for a given spatial dimension based on a localization criterion. Within the framework of the calculus of variations, we specify an Euler-Lagrange equation for this problem, and we find ...

IEEE Institute of Electrical and Electronics Engineers2015